# Reflexive relation, Symmetric relation and Transitive relation

Let X be defined between [0, 1] defined functions range. Describe what properties (Reflexive relation, Symmetric relation and Transitive relation) has relation R in group X, if $$fRg\Leftrightarrow\forall x\in[0,1],f(x)\neq g(x)$$

I have tried to solve it on my own, is it right to say that this isn't reflexive, because f(x)!=g(x)

• Correct, your logic shows non-reflexivity. What about the rest? – Teresa Lisbon Dec 12 '18 at 6:56

It isn't reflexive by your reasoning. It is symmetric (as $$f(x)\neq g(x)\Longleftrightarrow g(x)\neq f(x)$$) and non-transitive ($$f(x) \neq g(x)\ and\ g(x)\neq f(x)$$ but $$f(x)=f(x)$$).